3. For each of the following, evaluate IIs F ·nda, where n is the outward-pointing normal.

(a) S is the topological boundary of the rectangle [0,1] x [0,2] x [0,3] and F(x, y, z) = (x + eZ , y + eZ , eZ ).

(b) S is the truncated cylinder x2 + y2 = 1, ° :::; z :::; 1 together with the disks x2 + y2 :::; 1, z = 0,1, and F(x, y, z) = (x2, y2, Z2).

(c) S is the topological boundary of E, where E c R 3 is bounded by z = 2 - x2 , Z = x 2, Y = 0, z = y, and F(x,y,z) = (x+f(y,z),y+g(x,z),z+h(x,y))

and f,g,h: R2 -T Rare C1.

(d) S is the ellipsoid x2ja2 +y2jb2 +z2jc2 = 1 and F(x,y,z) = (xlyl,ylzl,zlxi).